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A proof of Haemers' toughness conjecture

math.CO · 2026-05-15 · accept · novelty 8.0

Proof that toughness t(Γ) ≥ μ₂ / (μₙ − δ) for connected graphs Γ with Laplacian eigenvalues 0 = μ₁ < μ₂ ≤ ⋯ ≤ μₙ and minimum degree δ.

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  • A proof of Haemers' toughness conjecture math.CO · 2026-05-15 · accept · none · ref 2

    Proof that toughness t(Γ) ≥ μ₂ / (μₙ − δ) for connected graphs Γ with Laplacian eigenvalues 0 = μ₁ < μ₂ ≤ ⋯ ≤ μₙ and minimum degree δ.